University:
Glendale Community College
Course:
MAT150 | College Algebra/Functions
Academic year:

2020
Views:

420

Pages:

23
Author:

Jamison Bradshaw

Section 6.6: Logarithmic and exponential equations #1 - 12: Solve the exponential equation by writing each side of the equation with the same base then equating the exponents. Problems also may be solved with logarithms. 1) 2x = 16 3) 2x+1 = 32 1 𝑥 5) ( ) = 16 2 7) 24−𝑥 = 64 9) 32x = 2 11) 16x = 4 #13 - 24: Solve the exponential equations, round your answer to 2 decimals. Steps: 1) Isolate the exponential function (when needed divide by the coefficient of the exponential function, only needed for problems 17, 18, 19 and 20) 2) Write in logarithmic form 3) Check 13) 3x = 6 Steps: 1) Isolate the exponential function (when needed divide by the coefficient of the exponential function, only needed for problems 17, 18, 19 and 20) 2) Write in logarithmic form (replace 𝑙𝑜𝑔𝑒 𝑤𝑖𝑡ℎ 𝑙𝑛 3) Check 15) ex = 12 Steps: 1) Isolate the exponential function (when needed divide by the coefficient of the exponential function, only needed for problems 17, 18, 19 and 20) 2) Write in logarithmic form 3) Check 17) 5(10x) = 20 Steps: 1) Isolate the exponential function (when needed divide by the coefficient of the exponential function, only needed for problems 17, 18, 19 and 20) 2) Write in logarithmic form 3) Check 19) 32e2x = 128 21) 3x-1 = 5 Steps: 1) Isolate the exponential function (when needed divide by the coefficient of the exponential function, only needed for problems 17, 18, 19 and 20) 2) Write in logarithmic form 3) Check Steps: 1) Isolate the exponential function (when needed divide by the coefficient of the exponential function, only needed for problems 17, 18, 19 and 20) 2) Write in logarithmic form 3) Check 23) 6x+4 = 9 #25 - 51: Solve the logarithmic equations, round to 2 decimals when needed. Steps (#25 – 38) 1) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 2) Solve for x 3) Check 25) log3 x = 2 Steps (#25 – 38) 1) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 2) Solve for x 3) Check 27) ln x = 1 Steps (#25 – 38) 1) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 2) Solve for x 3) Check 29) logx 49 = 2 (x >0) Steps (#25 – 38) 1) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 2) Solve for x 3) Check 31) logx 64 = 3 (x >0) Steps (#25 – 38) 1) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 2) Solve for x 3) Check 33) logx 3 = 1 2 (x>0) Steps (#25 – 38) 1) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 2) Solve for x 3) Check 35) log2 (x-1) = 3 Steps (#25 – 38) 1) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 2) Solve for x 3) Check 37) log2(2x)=5 Steps: (#39 – 42) 1) Drop the logs and set the arguments equal to each other. 2) Solve for x. 3) Check. 39) log (x+1) = log (3x–2) Steps: (#39 – 42) 1) Drop the logs and set the arguments equal to each other. 2) Solve for x. 3) Check. 41) log2 (x+3) = log2 (3x) Steps: (#43 – 47) 1) Use the minus to divide rule to write the left side with one logarithm. 2) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base to of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 3) Solve for x (you will need to cross multiply to solve) 4) Check 43) log2 x – log2 (x+6)=-2 Steps: (#43 – 47) 1) Use the minus to divide rule to write the left side with one logarithm. 2) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 3) Solve for x (you will need to cross multiply to solve) 4) Check 45) log2 x – log2 (x – 6) = 2 Steps: (#43 – 47) 1) Use the minus to divide rule to write the left side with one logarithm. 2) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 3) Solve for x (you will need to cross multiply to solve) 4) Check 47) log2 (x+6) – log2 (3x+2)=-1 1) Use the plus to times rule to write the left side with one logarithm. 2) Simplify the argument by performing the multiplication. 3) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 4) Solve for x (you will need set to equal zero and solve by factoring) 5) Check 49) log3 x + log3 (x+6) = 3 1) Use the plus to times rule to write the left side with one logarithm. 2) Simplify the argument by performing the multiplication. 3) Rewrite the problem in exponential form. • • • • Scratch out the log and create an exponential function. The base of the logarithm will be the base of the exponential function. Switch: make the number to the right of the equal sign an exponent place the argument to the right of the equal sign. 4) Solve for x (you will need set to equal zero and solve by factoring) 5) Check 51) log3 (x+6) + log3 (3x) = 4